DETROIT — The Red Sox need to win more than games over the next month and a half. They need to win over the front office.

Last night’s 5-3 victory over the Detroit Tigers was a good start, but it’s just a start.

General manager Ben Cherington broke in under Dan Duquette, and from the Duke to Mike Port to Theo Epstein to Cherington himself, the team’s last four GMs haven’t hesitated to pull the trigger on a July trade if they believed it would improve the club’s postseason chances.

But the Sox aren’t in the business of throwing resources at lost causes, and you’d better believe Cherington and Co. are weighing just how salvageable this season is as we speak.

So the team’s mandate is simple: Show the bosses signs of life, or what you see is what you’ll get.

“The way we’re playing, we definitely need help,” designated hitter David Ortiz said before slugging the game-winning, three-run homer in the ninth inning. “If you wait much longer, you’re going to be watching October from the beginning of August.”

First baseman Mike Napoli’s return from the disabled list last night helped, and right fielder Shane Victorino is possibly only two weeks away, too.

That means it’s go time. The Red Sox reside at the bottom of a very steep, very crowded hill. The only team in the American League with fewer wins is Tampa Bay, and that includes red-hot Houston, which has won 11-of-15 and nearly passed the Sox in the standings last night.

Even the players are sick of hearing how much time the Sox have, with 100 games remaining, because they still trail nine teams in the wild card standings.

“I hate using that,” left-hander Jon Lester said. “We used it a lot in ’11. We got off to that bad start and kept saying, ‘It’s early, it’s early, it’s early.’ You realize how important those games are at the end of the year with what happened then.”

So which way will the front office go? The belief in the organization is that the Red Sox are still capable of making a run. Recent history effectively illustrates how management approaches the trade deadline. Winning teams get help. Overly flawed ones don’t.

In 2009, the Red Sox landed Victor Martinez and ended up in the postseason. A year later they weren’t serious contenders, so they added Jarrod Saltalamacchia in an under-the-radar deal designed to pay dividends in later seasons, which it did.

The 2011 Sox tried desperately to acquire a starter, but when a trade for Oakland right-hander Rich Harden fell through, they settled for Seattle lefty Erik Bedard.

Do we really need to discuss 2012? The front office hedged its bets and didn’t pursue serious upgrades, but probably regrets failing to become aggressive sellers. The Sox acquired lefty Craig Breslow, though, and watched him become one of manager John Farrell’s most trusted relievers a year later.

“Last year, we needed that arm,” Lester said. “We needed somebody that has some experience and can pitch in big games and pick up Buch. But really, if Buch stays healthy, what do you go and get? We went out and got Q (Quintin Berry), who was the extra guy in the playoffs. That’s one thing that our ownership has always told us and followed through with: When we’re making a push, they’re going to make sure we have everything there to make that push.”

It’s on the players to give ownership a reason to believe.

“Absolutely,” Lester said. “Look at Kansas City. They fire their hitting coach. They’ve had four in the last three years or whatever. It’s not the hitting coach’s fault, just like in 2012 it wasn’t (pitching coach) Bob McClure’s fault that we stunk as a pitching staff. That was our fault. Obviously it’s a little easier to replace those guys than us sometimes.

“So yeah, that’s on us. That’s on these guys, these 25 guys that contribute every night. We’ve got to put ourselves in that position. We put ourselves in that position last year and got Peavy. The front office can make all the moves they want, but it’s our job to go out there and put up W’s.”

Maybe last night was a start. They’d best keep it going, or they’ll be waiting for help that never arrives.